Math Sabah Trial Pmr 2009 Paper 2

NAMA : ___________________

SULIT

KELAS : ___________________

JABATAN PELAJARAN NEGERI SABAH

PENILAIAN MENENGAH RENDAH 2009

50/2

MATHEMATICS 2 OGOS 2009 1 JAM 45 MINIT

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2 3

SATU JAM EMPAT PULUH LIMA MINIT

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Untuk Kegunaan Pemeriksa Soalan Markah Markah Tulis nama, tingkatan, nombor kad pengenalan Penuh Diperoleh dan angka giliran anda pada ruang yang 1 2 disediakan. 2 2 3 3 Kertas soalan ini adalah dalam dwi bahasa. 4 3 5 2 Calon dikehendaki membaca maklumat di 6 2 halaman belakang kertas soalan ini. 7 2 8 3 9 3 10 3 11 2 12 2 13 3 14 2 15 5 16 3 17 3 18 6 19 5 20 4 Jumlah Kertas soalan ini mengandungi 18 halaman bercetak

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MATHEMATICAL FORMULAE RUMUS MATEMATIK The following formulae may be helpful in answering the questions. The symbols given are commonly used. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. RELATIONS PERKAITAN

1

a m × a n = a m+n

2

a m ÷ a n = a m–n

3

(am)n = am n

4

Distance / Jarak =

5

Midpoint / Titik Tengah x1  x 2 y1  y 2 , 2 2

(x , y) =

6

Average speed =

Purata laju =

7

Mean =

Min

8

=

( x 2  x1 ) 2  ( y 2  y1 ) 2

distance travelled time taken jarak yang dilalui masa yang diambil

sum of data number of data hasil tambah nilai data bilangan data

Pythagoras Theorem / Teorem Pithagoras c2 = a2 + b2

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SHAPES AND SPACE BENTUK DAN RUANG 1

Area of rectangle = length × width Luas segiempat tepat = panjang × lebar

2

Area of triangle = Luas segitiga =

1 × base × height 2 1 × tapak × tinggi 2

3

Area of parallelogram = base × height Luas segiempat selari = tapak × tinggi

4

Area of trapezium = Luas trapezium =

1 × sum of parallel side × height 2

1 × hasil tambah dua sisi selari × tinggi 2

5

Circumference of circle =  d = 2  r Lilitan bulatan =  d = 2  j

6

Area of circle =  r 2 Luas bulatan =  j2

7

Curved surface area of cylinder = 2  rh Luas permukaan melengkung silinder = 2  jt

8

Surface area of sphere = 4  r2 Luas permukaan sfera = 4  j2

9

Volume of right prism = cross sectional area × length Isipadu prisma tegak = luas keratan rentas × panjang

10

Volume of cuboid = length × width × height Isipadu kuboid = panjang × lebar × tinggi

11

Volume of cylinder =  r2h Isipadu silinder =  j2t

12

Volume of cone =

1 2 rh 3

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Isipadu kon =

13

4 1 2 jt 3

Volume of sphere = Isipadu sfera =

14

4  r3 3

4  j3 3

Volume of right pyramid = Isipadu piramid tegak =

15

16

1 × base area × height 3

1 × luas tapak × tinggi 3

Sum of interior angles of a polygon = (n – 2) × 180° Hasil tambah sudut pedalaman poligon = (n – 2) × 180°

Arc length Circumference

=

Angle subtended at centre 360°

Panjang lengkok Sudut pusat = 360° Lilitan bulatan

17

Area of sector Area of circle Luas sektor Luas bulatan

=

=

Angle subtended at centre 360° Sudut pusat 360° PA΄ PA

18

Scale factor / Faktor skala, k =

19

Area of image = k2 × area of object Luas imej = k2 × luas objek

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Answer all questions. 1

Calculate the value of

1 2 2     and express the answer as a fraction in its lowest 6 3 9

For Examiner’s Use

terms. 1 2 2     dan ungkapkan jawapannya sebagai satu pecahan 6 3 9 dalam sebutan terendah. [2 marks] [2 markah]

Hitung nilai bagi

Answer / Jawapan:

1

2 2

0.36 and express the answer as a decimal. 0 .4 0.36 Hitung nilai bagi 2.3 + dan ungkapkan jawapannya dalam nombor 0 .4 perpuluhan.

Find the value of 2.3 +

[2 marks] [2 markah] Answer / Jawapan:

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6

(a) Find the value of Cari nilai bagi

3

For Examiner’s Use

1 . 125 1  . 125 3



2

3  (b) Calculate the value of   16  . 8  2

3  Hitung nilai bagi   16  . 8 

[3 marks] [3 markah] Answer / Jawapan:

3

3 4

Solve each of the following equations: Selesaikan tiap-tiap persamaan berikut: (a) y – 4 = – 9 (b) x – 3 =

1 x 3

[3 marks] [3 markah] Answer / Jawapan:

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Diagram 1 in the answer space shows object A and a straight line PQ drawn on a grid of equal squares. Rajah 1 di ruang jawapan menunjukkan objek A dan garis lurus PQ yang dilukis pada grid segiempat sama yang sama besar.

For Examiner’s Use

Draw the image of A under a reflection in the straight line PQ. Lukis imej bagi A di bawah pantulan pada garis lurus PQ. [2 marks] [2 markah] Answer / Jawapan :

P

A

Q

Diagram 1 Rajah 1

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Diagram 2 shows two polygons, M and M, drawn on a grid of equal squares with sides of 1 unit. Rajah 2 menunjukkan dua poligon, M dan M, yang dilukis pada grid segiempat sama bersisi 1 unit.

For Examiner’s Use

M M

M M

Diagram 2 Rajah 2 M is the image of M under transformation Z. M ialah imej bagi M di bawah suatu penjelmaan Z. Describe in full transformation Z. Huraikan selengkapnya penjelmaan Z. [2 marks] [2 markah] Answer / Jawapan:

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9

Factorise completely 12x2 – 27. Faktorkan selengkapnya 12x2 – 27.

For Examiner’s Use

[2 marks] [2 markah] Answer / Jawapan:

7

2 8

Expand each of the following expressions: Kembangkan tiap-tiap ungkapan berikut: (a) 3k ( f – 3 ). (b) (k + 3)2 – 2(3k – 1) [3 marks] [3 markah] Answer / Jawapan:

8

3 9

1 p3  as a single fraction in its simplest form. 3 p 12 p 2 1 p3 Ungkapkan  sebagai satu pecahan tunggal dalam bentuk termudah. 3 p 12 p 2 [3 marks] [3 markah] Answer / Jawapan: Express

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10 List all the integer values of k which satisfy both the inequalities 4 – k > 2 and 2k – 3 ≥ – 7 . Senaraikan semua nilai integer k yang memuaskan kedua-dua ketaksamaan 4 – k > 2 dan 2k – 3 ≥ – 7 . [3 marks] [3 markah] Answer / Jawapan:

For Examiner’s Use

10

3  11 In Diagram 3, y is the length of CD and cos x 

4 . 5

Dalam Rajah 3, y ialah panjang garis CD dan kos x 

4 . 5

AA

20 20 cm

12 cm 12

B

13 13 cm

x°x B

C

y y cm

D

D

Diagram 3 Rajah 3 Find the value of y. Cari nilai y.

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Answer / Jawapan:

3

12 Find the value of 3 2  3 3 2

Cari nilai bagi 3  3





1 2

1 2

For Examiner’s Use

.

. [2 marks] [2 markah]

Answer / Jawapan:

12

2 2

 12  13 Simplify  m n   n3 .   2

 12  Permudahkan  m n   n3 .   [2 marks] [2 markah] Answer / Jawapan:

13

2 14 Given that

p  q  t , express p in terms of q and t.

Diberi bahawa

p  q  t , ungkapkan p dalam sebutan q dan t.

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Answer/Jawapan:

15 Diagram 4 in the answer space is drawn on a square grid of sides 1 unit. W, X and Y are three moving points on the diagram. Rajah 4 di ruang jawapan yang dilukis pada segiempat grid yang bersisi 1 unit. W, X dan Y adalah tiga titik yang bergerak dalam rajah itu. (a)

For Examiner’s Use

W is a moving point such that it is always equidistant 2 units from the straight line KN. Describe in full the locus of W. W ialah titik yang bergerak dengan keadaan sama jarak 2 unit dari garis lurus KN. Huraikan sepenuhnya lokus W.

(b) On the diagram, draw Pada rajah itu, lukiskan (i) the locus of X such that AX = AD, lokus X dengan keadaan AX = AD, (ii) the locus Y such that BY = YD, lokus Y dengan keadaan BY = YD. (c) Hence, mark with the symbol  all the intersection of the locus of X and locus of Y. Seterusnya, tandakan dengan simbol  semua kedudukan bagi persilangan lokus X dan lokus Y itu. [5 marks] [5 markah] Answer/Jawapan: D

C

K

N

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B

A

Diagram 4 / Rajah 4 For Examiner’s Use

16 Diagram 5 shows a prism. Rajah 5 menunjukkan sebuah prisma.

5 units 2 units

4 units 4 units

Diagram 5 Rajah 5 Draw a full scale the net of the prism on the grid in the answer space. The grid has equal squares with side of 1 unit. Lukiskan skala penuh bentangan bagi prisma itu pada grid segiempat sama yang bersisi 1 unit di ruang jawapan. [3 marks] [3 markah] Answer / Jawapan:

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17 Table 1 shows the number of motorcycles repaired in three workshops. There are 80 motorcycles in the three workshops. Jadual 1 menunjukkan bilangan motosikal yang telah dibaiki bagi tiga buah bengkel. Terdapat 80 buah motosikal di ketiga-tiga bengkel tersebut. Workshop Bengkel

Number of motorcycles Bilangan motosikal

K

p

L

32

M

26

For Examiner’s Use

Table 1 Jadual 1 (a) Find the value of p. Cari nilai bagi p. (b) Hence, complete the bar chart to represent all the information in Table 1. Seterusnya, lengkapkan carta bar untuk mewakili semua maklumat dalam Jadual 1. [3 marks] [3 markah] Answer / Jawapan: Number of motorcycles Bilangan motosikal

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0

Workshop Bengkel

L

18 Set squares and protractors are not allowed to be used in section (a) of this question. Sesiku dan protraktor tidak boleh digunakan untuk ceraian (a) soalan ini. S

R

60° P

T Q Diagram 6 Rajah 6

Diagram 6 shows a rhombus PQRS. Rajah 6 menunjukkan sebuah rombus PQRS. (a) By using only a ruler and a pair of compasses, construct Diagram 6, beginning from the line PQ provided in the answer space. Dengan menggunakan pembaris dan jangka lukis sahaja, bina Rajah 6, bermula dengan garis lurus PQ yang disediakan di ruang jawapan. (b) Based on the diagram constructed in (a), measure the length of line ST. Berdasarkan rajah yang dibina di (a), ukur panjang garis lurus ST. [6 marks] [6 markah] Answer/Jawapan 50/2 © 2009 Copy right Sabah State Education Department

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Q

P

For Examiner’s Use

19 Table 2 shows the number of cars sold by a company in July 2009. Jadual 2 menunjukkan bilangan kereta yang telah dijual oleh sebuah syarikat dalam bulan Julai 2009. Model Model Perdana Waja Wira Iswara

Number of Cars Angle of Sector Bilangan Kereta Sudut Sektor 10 18 90° 20 100° 24 Table 2 Jadual 2

The information for Waja Model is shown fully in the pie chart in the answer space. Maklumat bagi model Waja ditunjukkan sepenuhnya dalam carta pai di ruang jawapan. Complete Lengkapkan (a) the angles of the sectors for Perdana Model and Iswara Model in Table 2. Sudut sektor bagi model Perdana dan model Iswara dalam Jadual 2. (b) the pie chart represents all the information in Table 2. carta pai itu untuk mewakili semua maklumat dalam Jadual 2. [5 marks] [5 markah] Answer / Jawapan:

Waja

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For Examiner’s Use

20 Table 3 shows the values of two variables, x and y of a function. Jadual 3 menunjukkan nilai-nilai pembolehubah x dan y bagi satu fungsi. x

−3

−2

−1

0

1

2

3

4

y

9

−2

9

−12

−11

−6

3

16

Table 3 Jadual 3 Draw the graph of the function using a scale of 2 cm to 1 unit on x-axis and 2 cm to 5 units on y-axis. Lukiskan graf fungsi itu dengan menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 2 cm kepada 5 unit pada paksi-y. [4 marks] [4 markah] Answer/Jawapan: 20

4

END OF QUESTION PAPER

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INFORMATION FOR CANDIDATES

1.

This questions paper consists of 20 questions.

2.

Answer all questions.

3.

Write your answers in the spaces provided in the question paper.

4.

Show your workings. It may help you to get marks.

5.

If you wish to change your answer, cross out the answer that you have done. Then write down the new answer.

6.

The diagrams in the questions provided are not drawn to scale unless stated.

7.

The marks allocated for each question are shown in brackets.

8.

A list of formulae is provided on pages 2 and 4.

9.

The usage of calculator is not allowed.

10. Hand in this question paper to the invigilator at the end of the examination.

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Marking Scheme PMR SABAH TRIAL 2009 MATHEMATICS P2 ,50/2 No 1.

2.

Solution and Marking Scheme

Sub Mark K1

Full Mark

3 8

N1

2

0.9

K1

3.2

N1

1 5

N1

4 9 or 9 24

2

3. (a)

–

(b)

3 3 12  4 or or 8 2 8 9 or 2.25 4

4. (a)

–5

(b)

3x + x = 1 + 9 or 4x = 10

K1

N1

3

N1

x=

5 or 2.5 2

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K1

N1

3

No

Solution and Marking Scheme

Sub Mark

Full Mark

Correct and complete drawing.

N2

2

Note: 1. Award N1 for correct image drawn using dotted line. 1 2. Allow gaps or extension line  of the square grid. 4 Translation / Translasi

P1

5.

Q

A

P

6.

 9     3

P1

3(4x29)

K1

3(2x + 3)(2x3)

N1

2

7.

2

Note : Direct correct answer award K1N1 8. (a)

3kf – 9k

(b)

k2 + 6k + 9

N1 or

 6k + 2

k2 + 11

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K1 N1

3

No 9.

Solution and Marking Scheme 4 p (1) p  3  12 p 2 12 p 2 4p p3 12 p 2

or

or

12 p 2 (1) 3 p( p  3)  36 p 3 36 p 2 12 p 2  3 p 2  9 p 36 p 3

p 1 4 p2 10.

Sub Mark

Full Mark

K1

K1

N1

k < 2 or 2 > k

K1

k≥ –2

K1

–2, –1,0,1

N1

3

3

Note : For – 2 ≤ k < 2 without answer K1K1N0 11.

4 BD  5 20

N1

3 1  2 2

P1

3

14.

K1

BC = 5

y = 11 12.

13.

or

9

N1

mn 2

K1

mn5

N1

p tq p  t  q 

or 2

or

tq 

p

P1

p  t 2  2tq  q 2

N1

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2

3

2

No 15. (a)

Solution and Marking Scheme

Two parallel lines from KN, 2 units.

Sub Mark

Full Mark

P2

Note: Parallel or correct locus drawn award P1. (b) (i)

Locus of X drawn correctly.

K1

(ii)

Locus of Y drawn correctly.

K1

(c)

The intersection of locus X and locus Y marked correctly.

N1 5

Note: Deduct 1 mark if using dotted lines or by sketching.

16.

N3

3

Note: 1. Any 2 surfaces drawn correctly award K1. 2. Another 2 surfaces drawn correctly award K1. 17. (a) (b)

22

P1

Each bar drawn correctly: Bar K Bar M

P1 P1

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No

Solution and Marking Scheme

18. (a)

Construct 60 at point P correctly.

K1

Draw line PS (Arc at PS).

K1

Intersection of two arcs to get point R.

K1

Draw PQRS.

K1

Construct perpendicular to line PQ from S.

K1

5.0  0.1 cm.

N1

(b)

Sub Mark

Full Mark

6

19.

Wira

Waja

100 120

50

Perdana

Iswara

1. Perdana = 50°

N1

2. Iswara = 120°

N1

3. Any one sector drawn correctly.

K1

4. Another one sector drawn.

K1

5. Pie chart drawn and labelled completely.

N1

20. (a)

Uniform scale on y-axis in the range  12  Y  16 .

K1

(b)

All 8 points correctly plotted.

K2

(c)

Smooth curve passes through all the 8 points.

N1

Note: 6 or 7 points correctly or passes through 6 or 7 points, award K1.

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5

4